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When an apple falls to the earth, by what process is its potential energy converted to kinetic energy? Gravitational processes alone. Apple-earth collisions p

by evanb 9y ago

When an apple falls to the earth, by what process is its potential energy converted to kinetic energy? Gravitational processes alone. Apple-earth collisions primarily radiate apple sauce, black hole mergers primarily radiate in gravitational energy. Minor nit: In general relativity black holes are not actually comprised of matter---they're entirely warping of spacetime. Whether that remains true in a quantum theory of gravity is unknown.

spuz 9y ago
None of this actually answers the question. The question is by what process does energy in the binary black hole system get converted into gravitational wave energy?
- T-A 9y ago
  If you accelerate an electric charge, it emits electromagnetic waves. If you accelerate a mass, it emits gravitational waves. Two masses orbiting their common center of gravity are undergoing centripetal acceleration, so they continuously emit gravitational waves, spiraling closer as they lose energy (that's how the emission of gravitational waves was originally confirmed [1]). [1] https://www.nobelprize.org/nobel_prizes/physics/laureates/1993/speedread.html https://www.nobelprize.org/nobel_prizes/physics/laureates/19...
- evanb 9y ago
  The answer is "by the processes of general relativity". When things fall "down" their potential energy is lowered, so they get faster. When mass-energy accelerates it emits gravitational waves, in much the same way when an electron accelerates it emits electromagnetic waves. If you're satisfied that a radio works by sloshing electrons around, you should be satisfied that a black hole merger emits radiation by sloshing mass around. Where did the photons "come from"? Well, they weren't stored "inside" the electrons. By what process were the photons generated? Electrons accelerating radiate. That's essentially the answer. You can "math it up" if you want. It's not exactly an axiom, but it's pretty close to the bottom.
  - evanb 9y ago
    Maybe I should be more clear: at least in the generally relativistic conception of gravity, all of the mass of the black hole "comes from" the warping of spacetime already. That's why I keep dancing around the question of whether it's "really" the kinetic energy or the mass or a mix that gets converted---it's hard to distinguish and may not be meaningful to distinguish the pieces from one another, especially if I go to a co-rotating frame.
    - raverbashing 9y ago
      > all of the mass of the black hole "comes from" the warping of spacetime already No, it's the other way around. The warping is due to the mass But the other answer hinted at the source: accelerating mass turns into gravitational waves as an accelerating electron turns into EM waves (remember rotation and things stopping abruptly also means acceleration) So yeah, it's the potential energy that turns into (less than Newtonian amounts of) kinetic energy because some of it is turning into Gravitational waves And you can imagine something as big as black holes spinning around each other at a frequency measurable in Hz how much energy they can give in that process then add the sudden merger deceleration.
      - improbable22 9y ago
        Certainly normal matter (like the earth) has mass and warps spacetime. But a black hole is a purely gravitational object, there need not be any normal matter involved. The mass of a black hole is something that's really only defined from a distance away. If a planet of 1 earth-mass orbits it at the same speed & circumference as we do the sun, then we say the black hole has 1 solar mass.
        raverbashing 9y ago
        > But a black hole is a purely gravitational object, there need not be any normal matter involved. There's no "purely gravitational object" it only "looks like that" from behind the event horizon We know the escape velocity > c and that's pretty much it, for GR it's a singularity (which usually means the theory is incomplete in that circumstance) and we don't know how QM work when squeezed harder than a Neutron star > The mass of a black hole is something that's really only defined from a distance away. If you mean "we can sense the gravitational field of something having mass X at a distance D larger than the event horizon" I agree. But I'd rather say "we don't know what happens there" instead of "singularity" (which is what the current theories say it's inside and from the point of view of Relativity they're not wrong)
raattgift 9y ago
The apple sauce line is amusing, and I'm sure you know all the following, but even in Newtonian mechanics, potential and kinetic energies are frame dependent; for example the latter is rotationally but not Galilean invariant. In modern gravitational physics you can treat components of the Einstein or stress-energy tensors as like these energies, e.g. for a family of observers, the apple-breaking kinetic energy is like the pressure components (T^ij, i=j, i!=0 ~ \gamma mv^2) and mostly in T^zz or T^rr or whichever, depending on one's choice of system of coordinates. However, simply by changing frame of reference, at each point where we find the apple/applesauce transition we can shuffle the whole of T^zz into one or more of the other components in G = T (keeping that relation invariant), and it is really stretching things to suggest that a change of coordinates is a process in the sense of the question in your first sentence. > In general relativity black holes are not actually comprised of matter---they're entirely warping of spacetime Well, that's not true of stellar collapse black holes; whatever you want to make of the trapping surface / apparent horizon, it encloses matter that existed before that formed. You don't need quantum anything, or even any future infalling, to deal with the fact that there is real matter inside at the time of formation. The Schwarzschild vacuum solution is matter-free, but then astrophysical black holes of all masses and all origins generally do not truly source the Schwarzschild metric, just a usefully close approximation. What you can say is that whatever's inside a black hole, eventually it will bald all its "hair" and can be effectively described (by an outside observer) at any point in time in terms of its spatial position (3 components), linear momentum (3 components), angular momentum (3 components), electromagnetic charge (1 component), and mass (1 component), with any other features irrelevant in the Kenneth Wilson sense. That is, eventually it doesn't matter whether it was all neutron degenerate matter or whether there were some other particles inside the horizon when it formed, but there was some matter there: the apparent horizon around V616 Monocerotis didn't just pop up spontaneously far from any matter. Quantum gravity only matters if you want to make guesses about what state the matter is in within the horizon (assuming you're unhappy about it inevitably being crunched into an infinitesimal point as in classical General Relativity), or about what it looks like when during evaporation the horizon retreats far enough to expose that state. I'll assume you favour keeping unitarity in any solution to the AMPS firewalls problem, and would happily ditch the apparent validity of the EFT outside the horizon. :-)

by evanb 9y ago

spuz 9y ago

None of this actually answers the question. The question is by what process does energy in the binary black hole system get converted into gravitational wave energy?

T-A 9y ago
If you accelerate an electric charge, it emits electromagnetic waves. If you accelerate a mass, it emits gravitational waves. Two masses orbiting their common center of gravity are undergoing centripetal acceleration, so they continuously emit gravitational waves, spiraling closer as they lose energy (that's how the emission of gravitational waves was originally confirmed [1]). [1] https://www.nobelprize.org/nobel_prizes/physics/laureates/1993/speedread.html https://www.nobelprize.org/nobel_prizes/physics/laureates/19...
evanb 9y ago
The answer is "by the processes of general relativity". When things fall "down" their potential energy is lowered, so they get faster. When mass-energy accelerates it emits gravitational waves, in much the same way when an electron accelerates it emits electromagnetic waves. If you're satisfied that a radio works by sloshing electrons around, you should be satisfied that a black hole merger emits radiation by sloshing mass around. Where did the photons "come from"? Well, they weren't stored "inside" the electrons. By what process were the photons generated? Electrons accelerating radiate. That's essentially the answer. You can "math it up" if you want. It's not exactly an axiom, but it's pretty close to the bottom.
- evanb 9y ago
  Maybe I should be more clear: at least in the generally relativistic conception of gravity, all of the mass of the black hole "comes from" the warping of spacetime already. That's why I keep dancing around the question of whether it's "really" the kinetic energy or the mass or a mix that gets converted---it's hard to distinguish and may not be meaningful to distinguish the pieces from one another, especially if I go to a co-rotating frame.
  - raverbashing 9y ago
    > all of the mass of the black hole "comes from" the warping of spacetime already No, it's the other way around. The warping is due to the mass But the other answer hinted at the source: accelerating mass turns into gravitational waves as an accelerating electron turns into EM waves (remember rotation and things stopping abruptly also means acceleration) So yeah, it's the potential energy that turns into (less than Newtonian amounts of) kinetic energy because some of it is turning into Gravitational waves And you can imagine something as big as black holes spinning around each other at a frequency measurable in Hz how much energy they can give in that process then add the sudden merger deceleration.
    - improbable22 9y ago
      Certainly normal matter (like the earth) has mass and warps spacetime. But a black hole is a purely gravitational object, there need not be any normal matter involved. The mass of a black hole is something that's really only defined from a distance away. If a planet of 1 earth-mass orbits it at the same speed & circumference as we do the sun, then we say the black hole has 1 solar mass.
      - raverbashing 9y ago
        > But a black hole is a purely gravitational object, there need not be any normal matter involved. There's no "purely gravitational object" it only "looks like that" from behind the event horizon We know the escape velocity > c and that's pretty much it, for GR it's a singularity (which usually means the theory is incomplete in that circumstance) and we don't know how QM work when squeezed harder than a Neutron star > The mass of a black hole is something that's really only defined from a distance away. If you mean "we can sense the gravitational field of something having mass X at a distance D larger than the event horizon" I agree. But I'd rather say "we don't know what happens there" instead of "singularity" (which is what the current theories say it's inside and from the point of view of Relativity they're not wrong)

raattgift 9y ago

The apple sauce line is amusing, and I'm sure you know all the following, but even in Newtonian mechanics, potential and kinetic energies are frame dependent; for example the latter is rotationally but not Galilean invariant. In modern gravitational physics you can treat components of the Einstein or stress-energy tensors as like these energies, e.g. for a family of observers, the apple-breaking kinetic energy is like the pressure components (T^ij, i=j, i!=0 ~ \gamma mv^2) and mostly in T^zz or T^rr or whichever, depending on one's choice of system of coordinates. However, simply by changing frame of reference, at each point where we find the apple/applesauce transition we can shuffle the whole of T^zz into one or more of the other components in G = T (keeping that relation invariant), and it is really stretching things to suggest that a change of coordinates is a process in the sense of the question in your first sentence. > In general relativity black holes are not actually comprised of matter---they're entirely warping of spacetime Well, that's not true of stellar collapse black holes; whatever you want to make of the trapping surface / apparent horizon, it encloses matter that existed before that formed. You don't need quantum anything, or even any future infalling, to deal with the fact that there is real matter inside at the time of formation. The Schwarzschild vacuum solution is matter-free, but then astrophysical black holes of all masses and all origins generally do not truly source the Schwarzschild metric, just a usefully close approximation. What you can say is that whatever's inside a black hole, eventually it will bald all its "hair" and can be effectively described (by an outside observer) at any point in time in terms of its spatial position (3 components), linear momentum (3 components), angular momentum (3 components), electromagnetic charge (1 component), and mass (1 component), with any other features irrelevant in the Kenneth Wilson sense. That is, eventually it doesn't matter whether it was all neutron degenerate matter or whether there were some other particles inside the horizon when it formed, but there was some matter there: the apparent horizon around V616 Monocerotis didn't just pop up spontaneously far from any matter. Quantum gravity only matters if you want to make guesses about what state the matter is in within the horizon (assuming you're unhappy about it inevitably being crunched into an infinitesimal point as in classical General Relativity), or about what it looks like when during evaporation the horizon retreats far enough to expose that state. I'll assume you favour keeping unitarity in any solution to the AMPS firewalls problem, and would happily ditch the apparent validity of the EFT outside the horizon. :-)